Question: Rewrite as a simplified fraction. ${1.91\overline{8} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1918.8888...\\ 100x &= 191.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1727}$ ${x = \dfrac{1727}{900}} \text{or} {1 \dfrac{827}{900}}$